Generalizations of polylogarithms for Feynman integrals

TL;DR

This paper reviews recent advances in using generalized polylogarithms, including elliptic versions, to compute complex multi-loop Feynman integrals, highlighting the Maple program MPL and applications to the sunrise integral.

Contribution

It introduces elliptic generalizations of polylogarithms and demonstrates their utility in calculating two-loop Feynman integrals, expanding the computational toolkit.

Findings

MPL supports computation of Feynman integrals with multiple polylogarithms

Elliptic polylogarithms are effective for massive two-loop sunrise integrals

Advances facilitate symbolic computation of complex multi-loop integrals

Abstract

In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the computation of Feynman integrals in terms of multiple polylogarithms. Furthermore we discuss elliptic generalizations of polylogarithms which have shown to be useful in the computation of the massive two-loop sunrise integral.